Correlations

Section I: Set-Up and Summary of the Dataset

First, we read in the data and set it up for analysis. The data is mostly cleaned, but we need a subset for calculating correlation, we need to change some data to be categorical, some data to be numerical, and we need to fix the dates so that they aren’t read in as characters.

Without doing anything, our dataset is as follows:

After cleaning, our main dataset is described below:

Our secondary dataset (used to measure correlation) is described below:

Section II: Descriptive Statistics

Section III: Plots and Graphs

Scatter Plot for Price and Number of Reviews

Scatter plot for price and number of reviews:

library(ggplot2)
library(ggpubr)
ggplot(airbnb, aes(x=price, y=number_of_reviews,)) + ggtitle("Number of Reviews vs Price Scatter Plot") + xlab("Price ($)") + ylab("Number Of Reviews") + geom_point(size = 1, shape = 18, color = "black") + geom_smooth(method = lm, se = FALSE, color = "yellow", size = 1.2) + theme_bw() + stat_cor(method =  "pearson", label.x = 7500 )

Box Plot for Price and Neighborhood Group

library(ggplot2)
ggplot(airbnb, aes(price, factor(neighbourhood_group))) + geom_boxplot(width = 0.7, color = "black", fill = c("light green", "pink","light blue", "yellow", "red")) +labs(title = "Neighbourhood group vs Price Box plot", x = "Price", y = "Neighbourhood")

Box Plot for Price and Room Type

library(ggplot2)
ggplot(airbnb, aes(price, factor(room_type))) + geom_boxplot(width = 0.7, color = "black", fill = c("light green", "yellow","light blue")) +labs(title = "Room type vs Price Box plot", x = "Price", y = "Room Type")

Map of NY by Price

Option 1:

library(ggmap)
library(tmaptools)
library(tidyr)
ggmap(get_stamenmap(rbind(as.numeric(paste(geocode_OSM("New York")$bbox))), zoom = 10)) + 
  geom_point(data = airbnb, aes(x = longitude, y = latitude, colour = neighbourhood_group, size = price), alpha = 0.2)

Option 2:

# create subset just for aggregating by mean
airbnb_map <- airbnb[ , c(6, 7, 8, 10)]
airbnb_map_means <- aggregate(.~neighbourhood, airbnb_map, mean)

# create subset for aggregating by count
airbnb_count <- airbnb_map
airbnb_count$count <- 1
airbnb_count <- airbnb_count[, c(1,5)]
airbnb_counter <- aggregate(.~neighbourhood, airbnb_count, sum)

# create full dataset from both subsets
airbnb_map_full <- cbind(airbnb_counter, airbnb_map_means)

# check that union occured correctly, then drop extra neighborhood value
all.equal(airbnb_map_full[, 1], airbnb_map_full[, 3])

## [1] TRUE

airbnb_map_full <- airbnb_map_full[, -3]

library(ggmap)
library(tmaptools)
library(tidyr)
ggmap(get_stamenmap(rbind(as.numeric(paste(geocode_OSM("New York")$bbox))), zoom = 10)) + 
  geom_point(data = airbnb_map_full, aes(x = longitude, y = latitude, colour = price, size = count), alpha = 0.5) + scale_colour_gradientn(colours=rainbow(3))

# Section IV: Correlation and ANOVA Tests

Correlation

Correlation Matrix for Airbnb Data

loadPkg("faraway")
loadPkg("corrplot")
xkabledply(cor(airbnb_cor))

Table

	price	minimum_nights	number_of_reviews	reviews_per_month	calculated_host_listings_count	availability_365
price	1.0000	0.0428	-0.0480	NA	0.0575	0.0818
minimum_nights	0.0428	1.0000	-0.0801	NA	0.1280	0.1443
number_of_reviews	-0.0480	-0.0801	1.0000	NA	-0.0724	0.1720
reviews_per_month	NA	NA	NA	1	NA	NA
calculated_host_listings_count	0.0575	0.1280	-0.0724	NA	1.0000	0.2257
availability_365	0.0818	0.1443	0.1720	NA	0.2257	1.0000

airbnb_corplot = cor(airbnb_cor, use = "complete.obs")
corrplot(airbnb_corplot, method = "circle")

No strong correlations with price, but minimum_nights and availability_365, number_of_reviews and availability_365, and calculated_host_listings_count and availability_365 show some evidence of positive correlation.

Correlation Between Reviews per Month and Total Reviews

plot(x=airbnb_cor$reviews_per_month, y=airbnb_cor$number_of_reviews)

cor.test(x=airbnb_cor$reviews_per_month, y=airbnb_cor$number_of_reviews)

## 
##  Pearson's product-moment correlation
## 
## data:  airbnb_cor$reviews_per_month and airbnb_cor$number_of_reviews
## t = 130, df = 38841, p-value <2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.543 0.557
## sample estimates:
##  cor 
## 0.55

As expected, correlated since reviews per month is a function of total number of reviews so do not need to look at both.

Correlation Between Number of Reviews (Y) and Price (X)

plot(y=airbnb$number_of_reviews, x=airbnb$price)

cor.test(y=airbnb$number_of_reviews, x=airbnb$price)

## 
##  Pearson's product-moment correlation
## 
## data:  airbnb$price and airbnb$number_of_reviews
## t = -11, df = 48893, p-value <2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.0568 -0.0391
## sample estimates:
##    cor 
## -0.048

No evidence of strong (linear) correlation, but evidence of an inverse relationship between price and reviews (higher price, fewer reviews–possibly because of fewer stays, for which review number is probably a good proxy)

ANOVA Tests

Testing for Differences in Price by Neighborhood Group

#anova test for price and neighborhood groups
anova_price_group = aov(price ~ neighbourhood_group, data=airbnb)
anova_price_group

## Call:
##    aov(formula = price ~ neighbourhood_group, data = airbnb)
## 
## Terms:
##                 neighbourhood_group Residuals
## Sum of Squares             7.96e+07  2.74e+09
## Deg. of Freedom                   4     48890
## 
## Residual standard error: 237
## Estimated effects may be unbalanced

summary(anova_price_group) -> sum_anova_price_group
xkabledply(sum_anova_price_group, title = "ANOVA result summary for Neighborhood Groups")

ANOVA result summary for Neighborhood Groups

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
neighbourhood_group	4	7.96e+07	19897739	355	0
Residuals	48890	2.74e+09	56051	NA	NA

tukeyAoV_pg <- TukeyHSD(anova_price_group)
tukeyAoV_pg

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = price ~ neighbourhood_group, data = airbnb)
## 
## $neighbourhood_group
##                           diff     lwr   upr p adj
## Brooklyn-Bronx           36.89   16.81  57.0 0.000
## Manhattan-Bronx         109.38   89.34 129.4 0.000
## Queens-Bronx             12.02   -9.33  33.4 0.539
## Staten Island-Bronx      27.32  -11.42  66.1 0.305
## Manhattan-Brooklyn       72.49   66.17  78.8 0.000
## Queens-Brooklyn         -24.87  -34.58 -15.2 0.000
## Staten Island-Brooklyn   -9.57  -43.32  24.2 0.938
## Queens-Manhattan        -97.36 -106.99 -87.7 0.000
## Staten Island-Manhattan -82.06 -115.79 -48.3 0.000
## Staten Island-Queens     15.29  -19.23  49.8 0.746

Testing for Differences in Price by Room Type

#anova test for price and room type
anova_price_room = aov(price ~ room_type, data=airbnb)
anova_price_room

## Call:
##    aov(formula = price ~ room_type, data = airbnb)
## 
## Terms:
##                 room_type Residuals
## Sum of Squares   1.85e+08  2.63e+09
## Deg. of Freedom         2     48892
## 
## Residual standard error: 232
## Estimated effects may be unbalanced

summary(anova_price_room) -> sum_anova_price_room
xkabledply(sum_anova_price_room, title = "ANOVA result summary for Room Type")

ANOVA result summary for Room Type

	Df	Sum Sq	Mean Sq	F value	Pr(>F)
room_type	2	1.85e+08	92512441	1717	0
Residuals	48892	2.63e+09	53892	NA	NA

tukeyAoV_pr <- TukeyHSD(anova_price_room)
tukeyAoV_pr

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = price ~ room_type, data = airbnb)
## 
## $room_type
##                                diff  lwr     upr p adj
## Private room-Entire home/apt -122.0 -127 -117.02 0.000
## Shared room-Entire home/apt  -141.7 -158 -125.33 0.000
## Shared room-Private room      -19.7  -36   -3.27 0.014